Theoretical Probability worksheet - Free Printable

Let’s go through each event one by one and decide how likely it is — impossible, unlikely, equally likely, likely, or certain.

We’ll use the probability scale:
- 0 = Impossible
- ¼ = Unlikely
- ½ = Equally likely
- ¾ = Likely
- 1 = Certain

---

1) A two-sided coin is flipped and lands on heads.
→ Just like the example (tails), heads has a 50% chance → ½ -- Equally likely

2) Roll a die and get a number greater than six.
→ A standard die only goes up to 6 → You can’t roll higher → Impossible

3) Spin a spinner numbered 1-8, and you land on a number less than 3.
→ Numbers less than 3: 1 and 2 → That’s 2 out of 8 → 2/8 = ¼ → Unlikely

4) You will watch at least 1 hour of TV today.
→ This depends on your day — but since we don’t know, and many kids do watch some TV, it’s more probable than not → Let’s say Likely (but note: this is subjective — in class, teacher might accept “equally likely” too. We’ll go with likely as most students watch some TV.)

Actually — let’s think again. Since it’s about *you*, and no info given, maybe better to treat as uncertain. But in worksheets like this, they often expect real-world judgment. Most kids watch at least 1 hour? Probably yes → Likely

5) Pick a blue marble from an equal number of blue, yellow, red, and green marbles.
→ 4 colors, equal amounts → 1 out of 4 → ¼ → Unlikely

Wait — actually, if there are equal numbers, then probability of picking blue is 1/4 → which matches “unlikely” on the chart → Unlikely

But hold on — sometimes people think “equal chance among options” means equally likely — but here, since there are 4 choices, each has 25% chance → so yes, Unlikely

6) You will have fish for dinner tonight.
→ Again, depends — but unless told otherwise, assume it’s not guaranteed. Many families don’t eat fish every night → So probably Unlikely (unless you live near ocean or love fish — but generally, safe to say unlikely)

7) Pick an ace from a regular deck of cards.
→ Deck has 52 cards, 4 aces → 4/52 = 1/13 ≈ 0.077 → less than ¼ → So even less than unlikely? But our scale doesn’t go below ¼. Closest is Unlikely

Actually — 1/13 is about 7.7%, while ¼ is 25%. So definitely less than unlikely — but since “impossible” is 0, and this isn’t zero, we still call it Unlikely (as it’s possible but rare)

8) Pick a red card from a regular deck of cards.
→ Half the deck is red (hearts + diamonds) → 26/52 = ½ → Equally likely

9) Your class will go on a field trip this year.
→ Not guaranteed — schools plan them, but not always happen → Could be likely or unlikely depending on school. In general, many classes do go → Let’s say Likely

10) Roll a die and get an even number.
→ Even numbers: 2, 4, 6 → 3 out of 6 → ½ → Equally likely

11) Roll a die and get a number that is a factor of 30.
→ Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30 → On a die (1-6): 1, 2, 3, 5, 6 → That’s 5 numbers → 5/6 ≈ 0.83 → closer to 1 → Certain? No — not all numbers are factors (4 is missing). 5/6 is very high → Likely (since ¾ = 0.75, and 5/6 > 0.75)

Yes — 5/6 is about 83%, which is above 75% → so Likely

12) It will snow in your town tonight.
→ Depends where you live — but unless specified, assume average place — snow is not common every night → Unlikely (could be impossible in summer, but worksheet probably expects general answer)

In most places, snow tonight is not expected → Unlikely

13) Your birthday will fall on a Friday this year.
→ There are 7 days in a week → Each day has roughly 1/7 chance → ~14% → less than 25% → Unlikely

(Unless you already know your birthday date — but assuming random, it’s unlikely to be Friday specifically)

14) Pick a purple marble out of a bag of red marbles.
→ Only red marbles → No purple → Can’t happen → Impossible

15) Picking a vowel from the letters in your school’s name.
→ Vowels: A, E, I, O, U → School names vary — e.g., “Lincoln Middle School” → L,I,N,C,O,L,N,M,I,D,D,L,E,S,C,H,O,O,L → vowels: I,O,I,E,O,O → lots of vowels → probably more than half? Not necessarily.

But since we don’t know the school name, we must assume typical case. Most English words have vowels — often around 40-50%. For example, “School” → S,C,H,O,O,L → 2 vowels out of 6 → 1/3 → ~33% → between ¼ and ½ → closer to ½? Or call it Equally likely?

Wait — let’s take a common school name: “Washington Elementary”

W,A,S,H,I,N,G,T,O,N,E,L,E,M,E,N,T,A,R,Y → count vowels: A,I,O,E,E,E,A → 7 vowels? Total letters: let's not count exactly — but roughly, vowels are frequent.

Actually, in English text, vowels make up about 40% of letters. So 40% is between ¼ (25%) and ½ (50%). Closer to ½? Maybe call it Equally likely as approximation.

But strictly speaking, 40% is less than 50% — so perhaps Unlikely? No — 40% is closer to 50% than to 25%. And in educational contexts, they often round.

Alternatively, think: is it more likely than not to pick a vowel? In many names, yes — because consonants cluster, but vowels are spread.

To be safe — let’s say for most school names, probability is around 40-50% → so Equally likely is acceptable.

Some teachers might say “it depends”, but for worksheet, we’ll go with Equally likely

---

Now let’s compile final answers:

1) Equally likely
2) Impossible
3) Unlikely
4) Likely
5) Unlikely
6) Unlikely
7) Unlikely
8) Equally likely
9) Likely
10) Equally likely
11) Likely
12) Unlikely
13) Unlikely
14) Impossible
15) Equally likely

Double-checking tricky ones:

#5: Equal marbles of 4 colors → 1/4 → Unliable → Correct
#7: Ace in deck → 4/52=1/13≈7.7% → Unlikely → Correct
#11: Factors of 30 on die: 1,2,3,5,6 → 5/6≈83% → Likely → Correct
#15: Vowel in school name — assumed ~40-50% → Equally likely → Reasonable

Final Answer:
1) Equally likely
2) Impossible
3) Unlikely
4) Likely
5) Unlikely
6) Unlikely
7) Unlikely
8) Equally likely
9) Likely
10) Equally likely
11) Likely
12) Unlikely
13) Unlikely
14) Impossible
15) Equally likely